Finite Group Databasebeta

← Group #7001024

Character table — Group #7001024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222244444444444444444444444444444444888888888888888888888888816161616161616161616
order12222222444444442222224444444444888888888888888822444444444444444888888882444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-111-1-11-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-11
χ5111111111111111111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1111-111-1111-11111-1-111-1-1-1-1-1-11-11-1-1-11-1-1-1
χ6111111111111111111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-11-1111-1111
χ7111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-111-1-11111111-11-11-1-11-11
χ8111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1-11-11111-1-1-1-1111111-11-11-111-11-1
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1111-111-1111-1-111-1-111-1-1-1-1-1-1-11-1-1-111-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-11-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1111-1111-1-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11-1-1-111-11-1-111-1-111-1-11111-1-1-111-11-111
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-11111111-1-11-11-1-1
χ131111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-111111-1-111-1-1-1-1-1-1-1-11111-11-1-111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111-111-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-11-1-1-1111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11-1111-1-1-111
χ1711111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11-1-111111111-1-11111-1-11-1-11-11-1-1-11
χ1811111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-111-11-1111-1
χ1911111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-111-1-1-1-1-1-111-1-1-1-1111-1-111111-1-1
χ2011111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-1-111-111-1-1-1-1-111
χ2111111111-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-1-1-11111111111-11-1-1-1-1-11-11111-1-1-1-1-1-1-1-11111-1-11-1-111-1
χ2211111111-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1111-1111-1-1-1-1-111-1-1-1-1-1-111-1-111-111-1-11
χ2311111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1111-1-1-11-1-1-1-1-111111111-1-111-1-1-1-11-111
χ2411111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-11111-1-1111111-1-1-1-11111-11-1-1
χ2511111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1111111-1-111-11111-11-1-1-1
χ2611111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-111-11-1-111-1-11111-1-1111-1-1-1-11-1111
χ2711111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1111111111111111-111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1111-1-1-11-11
χ2811111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1111111111111-1-11-1-1-1-111-1111-1-111-1-1-1-111-1-11-1-1-1111-11-1
χ2911111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-111-1-1-1-111-1-111-1-1-1-11-1-111111
χ3011111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1111111-1-111-1-111-111-1-1-1-1-1
χ3111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-11111-1-111-1-111-1-11-111-1-11-1
χ3211111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-111-1-1-1-1-1-111-1-11111-11-1-111-11
χ33222222222222-2-2-2-22222-2-22222-2-22222000000000000000000-2-200-200-2-2000000000000000000000000
χ34222222222222-2-2-2-222-2-22222-2-2-2-2-2-2-2-2000000000000000000-2200200-22000000000000000000000000
χ35222222222222-2-2-2-2-2-22222-2-222-2-2-2-2-2-20000000000000000002-2002002-2000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000002200-20022000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-20000000000000000002200-200-2-2000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2220000000000000000002-200200-22000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000-22002002-2000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2000000000000000000-2-200-20022000000000000000000000000
χ41222-2-2-2-222i2i−2i−2i2-22-200000000002i−2i000022-2-22i2i−2i−2i000000002-2002i−2i02i−2i002-20000000000000000000000
χ42222-2-2-2-222i2i−2i−2i2-22-200000000002i−2i000022-2-22i2i−2i−2i00000000-2200−2i2i0−2i2i00-220000000000000000000000
χ43222-2-2-2-222i2i−2i−2i2-22-200000000002i−2i0000-2-222−2i−2i2i2i000000002-200−2i2i02i−2i00-220000000000000000000000
χ44222-2-2-2-222i2i−2i−2i2-22-200000000002i−2i0000-2-222−2i−2i2i2i00000000-22002i−2i0−2i2i002-20000000000000000000000
χ45222-2-2-2-22−2i−2i2i2i2-22-20000000000−2i2i000022-2-2−2i−2i2i2i000000002-200−2i2i0−2i2i002-20000000000000000000000
χ46222-2-2-2-22−2i−2i2i2i2-22-20000000000−2i2i000022-2-2−2i−2i2i2i00000000-22002i−2i02i−2i00-220000000000000000000000
χ47222-2-2-2-22−2i−2i2i2i2-22-20000000000−2i2i0000-2-2222i2i−2i−2i000000002-2002i−2i0−2i2i00-220000000000000000000000
χ48222-2-2-2-22−2i−2i2i2i2-22-20000000000−2i2i0000-2-2222i2i−2i−2i00000000-2200−2i2i02i−2i002-20000000000000000000000
χ492-22-222-2-22i−2i2i−2i00002-22-2002i−2i2i−2i002-22i−2ii2−i2i2−i22−22−2i2i2−i2−i222−2−2000000000000000002−2i2−i2i2−i22−20000000000
χ502-22-222-2-22i−2i2i−2i00002-22-2002i−2i2i−2i002-22i−2i−i2i2−i2i2−22−22−i2−i2i2i2−2−22200000000000000000−22−i2i2−i2i2−220000000000
χ512-22-222-2-22i−2i2i−2i00002-2-22002i−2i−2i2i00-22−2i2ii2−i2i2−i22−22−2i2i2−i2−i2−2−222000000000000000002−2−i2i2−i2i2−220000000000
χ522-22-222-2-22i−2i2i−2i00002-2-22002i−2i−2i2i00-22−2i2i−i2i2−i2i2−22−22−i2−i2i2i222−2−200000000000000000−22i2−i2i2−i22−20000000000
χ532-22-222-2-22i−2i2i−2i0000-222-200−2i2i2i−2i00-22−2i2ii2−i2i2−i22−22−2−i2−i2i2i222−2−200000000000000000−22i2−i2−i2i2−220000000000
χ542-22-222-2-22i−2i2i−2i0000-222-200−2i2i2i−2i00-22−2i2i−i2i2−i2i2−22−22i2i2−i2−i2−2−222000000000000000002−2−i2i2i2−i22−20000000000
χ552-22-222-2-22i−2i2i−2i0000-22-2200−2i2i−2i2i002-22i−2ii2−i2i2−i22−22−2−i2−i2i2i2−2−22200000000000000000−22−i2i2i2−i22−20000000000
χ562-22-222-2-22i−2i2i−2i0000-22-2200−2i2i−2i2i002-22i−2i−i2i2−i2i2−22−22i2i2−i2−i222−2−2000000000000000002−2i2−i2−i2i2−220000000000
χ572-22-222-2-2−2i2i−2i2i00002-22-200−2i2i−2i2i002-2−2i2ii2−i2i2−i2−22−22i2i2−i2−i2−2−22200000000000000000−22i2−i2i2−i2−220000000000
χ582-22-222-2-2−2i2i−2i2i00002-22-200−2i2i−2i2i002-2−2i2i−i2i2−i2i22−22−2−i2−i2i2i222−2−2000000000000000002−2−i2i2−i2i22−20000000000
χ592-22-222-2-2−2i2i−2i2i00002-2-2200−2i2i2i−2i00-222i−2ii2−i2i2−i2−22−22i2i2−i2−i222−2−200000000000000000−22−i2i2−i2i22−20000000000
χ602-22-222-2-2−2i2i−2i2i00002-2-2200−2i2i2i−2i00-222i−2i−i2i2−i2i22−22−2−i2−i2i2i2−2−222000000000000000002−2i2−i2i2−i2−220000000000
χ612-22-222-2-2−2i2i−2i2i0000-222-2002i−2i−2i2i00-222i−2ii2−i2i2−i2−22−22−i2−i2i2i2−2−222000000000000000002−2i2−i2−i2i22−20000000000
χ622-22-222-2-2−2i2i−2i2i0000-222-2002i−2i−2i2i00-222i−2i−i2i2−i2i22−22−2i2i2−i2−i222−2−200000000000000000−22−i2i2i2−i2−220000000000
χ632-22-222-2-2−2i2i−2i2i0000-22-22002i−2i2i−2i002-2−2i2ii2−i2i2−i2−22−22−i2−i2i2i222−2−2000000000000000002−2−i2i2i2−i2−220000000000
χ642-22-222-2-2−2i2i−2i2i0000-22-22002i−2i2i−2i002-2−2i2i−i2i2−i2i22−22−2i2i2−i2−i2−2−22200000000000000000−22i2−i2−i2i22−20000000000
χ65444-4-4-4-444i4i−4i−4i-44-440000000000−4i4i0000000000000000000000000000000000000000000000000000000
χ66444-4-4-4-44−4i−4i4i4i-44-4400000000004i−4i0000000000000000000000000000000000000000000000000000000
χ6744-4-44-44-40000000000004-40000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000
χ6844-4-44-44-40000000000004-4000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000
χ6944-4-44-44-4000000000000-440000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000
χ7044-4-44-44-4000000000000-44000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000
χ714-444-4-44-44-4-44000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ724-444-4-44-44-4-4400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ734-444-4-44-4-444-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ744-444-4-44-4-444-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ754-4-444-4-44000044-4-400000000000000000000000000004i−4i−4i4i00000000000000000000000000000000000
χ764-4-444-4-44000044-4-40000000000000000000000000000−4i4i4i−4i00000000000000000000000000000000000
χ774-4-444-4-440000-4-4440000000000000000000000004-4-44000000000000000000000000000000000000000
χ784-4-444-4-440000-4-444000000000000000000000000-444-4000000000000000000000000000000000000000
χ794-4-4-4-444400004-4-44000000000000000000000000000000000000000000000004-4000000000000000000
χ804-4-4-4-444400004-4-4400000000000000000000000000000000000000000000000-44000000000000000000
χ814-4-4-4-44440000-444-40000000000000000000000000000000000000000000004-400000000000000000000
χ824-4-4-4-44440000-444-4000000000000000000000000000000000000000000000-4400000000000000000000
χ8388-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).